Which of the following is equivalent to the complex number i^(7) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Step 1: Simplify i^(7): To solve for i^(7), we need to remember that i is the imaginary unit, which is defined by the property that i^2 = -1. We can use this property to simplify i^(7). i^(7) = i^(6) * i^(1) = (i^(2))^3 * i = (-1)^3 * i = -1 * i = -iStep 2: Match with given choices: Now that we have simplified i^(7) to -i, we can match this result with the given choices. (A) 1 (B) i (C) -1 (D) -i The correct answer is (D) -i.

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Which of the following is equivalent to the complex number
i^(7) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{7}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

Q. Which of the following is equivalent to the complex number

i^{7}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Step $1$ : Simplify $i^{7}$ : To solve for $i^{7}$ , we need to remember that $i$ is the imaginary unit, which is defined by the property that $i^2 = -1$ . We can use this property to simplify $i^{7}$ . $\newline$ $i^{7} = i^{6} \cdot i^{1}$ $\newline$ $= (i^{2})^{3} \cdot i$ $\newline$ $= (-1)^{3} \cdot i$ $\newline$ $= -1 \cdot i$ $\newline$ $= -i
Step $2$: Match with given choices: Now that we have simplified $i^{7}$ to $-i$, we can match this result with the given choices.$\newline$(A) $1$$\newline$(B) $i$$\newline$(C) $-1$$\newline$(D) $-i$$\newline$The correct answer is (D) $-i$.